The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A276085 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A276085

Primorial base log-function: fully additive with a(p) = p#/p, where p# = A034386(p).
(history; published version)

#77 by Michael De Vlieger at Wed Nov 13 13:53:22 EST 2024

STATUS

proposed

approved

#76 by Antti Karttunen at Wed Nov 13 10:28:03 EST 2024

STATUS

editing

proposed

#75 by Antti Karttunen at Wed Nov 13 09:23:12 EST 2024

CROSSREFS

Positions of multiples of k in this sequence, for k=2, 3, 4, 5, 8, 27, 3125: A003159, A339746, A369002, A373140, A373138, A377872, A377878.

#74 by Antti Karttunen at Wed Nov 13 08:25:46 EST 2024

CROSSREFS

Cf. A000040, A000720, A002110, A028234, A034386, A048103, A049345, A055396, A067029, A108951, A143293, A276154, A328316, A328624, A328625, A328768, A328832, A346105, A351576, A376398 (partial sums).

#73 by Antti Karttunen at Mon Nov 11 20:52:22 EST 2024

PROG

(PARI) A276085(n) = { my(f=factor(n)); sum(k=1, #f~, f[k, 2]*prod(i=1, primepi(f[k, 1]-1), prime(i))); }; \\ Antti Karttunen, Mar 15 2021, Jun 23 2024

CROSSREFS

Positions of multiples of k in this sequence, for k=2, 3, 4, 5, 8, 27: A003159, A339746, A369002, A373140, A373138, A377872.

#72 by Antti Karttunen at Mon Nov 11 20:50:37 EST 2024

PROG

(PARI) A276085(n) = { my(f = factor(n), pr=1, i=1, s=0); for(k=1, #f~, while(i <= primepi(f[k, 1])-1, pr *= prime(i); i++); s += f[k, 2]*pr); (s); }; \\ Antti Karttunen, Nov 11 2024

STATUS

approved

editing

#71 by Michael De Vlieger at Sun Jun 23 10:32:36 EDT 2024

STATUS

proposed

approved

#70 by Antti Karttunen at Sun Jun 23 07:38:23 EDT 2024

STATUS

editing

proposed

#69 by Antti Karttunen at Sun Jun 23 04:07:27 EDT 2024

PROG

(PARI) A276085(n) = { my(f=factor(n)); sum(k=1, #f~, f[k, 2]*prod(i=1, primepi(f[k, 1]-1), prime(i))); }; \\ _Antti Karttunen_, Mar 15 2021, Jun 23 2024

A002110(n) = prod(i=1, n, prime(i));

A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*A002110(primepi(f[k, 1])-1)); }; \\ Antti Karttunen, Mar 15 2021

(PARI) A276085(n) = { my(f=factor(n)); sum(k=1, #f~, f[k, 2]*prod(i=1, primepi(f[k, 1]-1), prime(i))); }; \\ Antti Karttunen, Jun 23 2024

#68 by Antti Karttunen at Sun Jun 23 03:57:01 EDT 2024

PROG

(PARI) A276085(n) = { my(f=factor(n)); sum(k=1, #f~, f[k, 2]*prod(i=1, primepi(f[k, 1]-1), prime(i))); }; \\ Antti Karttunen, Jun 23 2024