A351553 - OEIS

A351553

Even numbers k such that there are no odd prime factors p of k such that p would not divide A003961(k) and the valuation(k, p) would be different from valuation(sigma(k), p), where A003961 is fully multiplicative with a(p) = nextprime(p), and sigma is the sum of divisors function.

2, 6, 10, 14, 20, 22, 24, 28, 30, 34, 40, 42, 46, 54, 60, 62, 66, 70, 84, 94, 102, 106, 110, 114, 120, 130, 138, 140, 142, 154, 160, 168, 170, 174, 182, 186, 190, 198, 210, 214, 216, 220, 224, 230, 238, 254, 260, 264, 270, 280, 282, 290, 308, 310, 318, 322, 330, 340, 354, 374, 378, 380, 382, 390, 408, 410, 420, 426

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OFFSET

1,1

COMMENTS

Even numbers k for which A351555(k) = 0.

LINKS

Table of n, a(n) for n=1..68.

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

PROG

(PARI)

A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; A351555(n) = { my(s=sigma(n), f=factor(s), u=A003961(n)); sum(k=1, #f~, if((f[k, 1]%2) && 0!=(u%f[k, 1]), (valuation(n, f[k, 1])!=f[k, 2]), 0)); };

isA351553(n) = (!(n%2) && 0==A351555(n));

CROSSREFS

Cf. A000203, A005820, A003961, A046060, A351552.

Even terms in A351554, positions of zeros at even indices in A351555.

Cf. A351543 (complement among even numbers).

Sequence in context: A284678 A367367 A185548 * A354715 A239221 A039956

Adjacent sequences: A351550 A351551 A351552 * A351554 A351555 A351556

KEYWORD

nonn

AUTHOR

Antti Karttunen, Feb 16 2022

STATUS

approved