A260021 Solutions to phi(n) = phi(sigma(n)) that are not given by Theorem 3 of Golomb's manuscript.

1, 3, 15, 45, 175, 357, 585, 608, 646, 962, 1071, 1292, 1443, 1508, 1586, 1664, 1665, 1898, 2275, 2295, 2379, 2745, 2847, 3285, 3848, 4082, 4329, 4514, 4641, 4736, 4845, 5018, 5402, 6123, 6232, 6344, 6475, 6771, 7052, 7065, 7137, 7202, 7215, 7527, 7592, 7803, 7808, 8103, 8138, 8398, 8541, 8685, 8906, 9344, 9526, 10322

Offset: 1

Author

N. J. A. Sloane, Jul 14 2015

Keywords

• nonn

References

• S. W. Golomb, Equality among number-theoretic functions, Manuscript, no date; Second update, Dec 29, 1992.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• S. W. Golomb, Equality among number-theoretic functions, Unpublished manuscript. (Annotated scanned copy)
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..103800
• Index entries for sequences related to sigma(n)

Crossrefs

Setwise difference A006872 \ A354345. Subset of positions of zeros in A353636.

Cf. A354362 (subsequence).

Cf. also A005383, A353637, A354344.

Programs

PARI

A354344(n) = { if(!(n%15),n/=15,if(!(n%9),n/=9,if(!(n%8),n/=8,if(!(n%3),n/=3,if(!(n%2),n/=2,return(0)))))); ((n>5) && isprime(n) && isprime((1+n)/2)); };
A353637(n) = (eulerphi(sigma(n))==eulerphi(n));
isA260021(n) = (A353637(n) && !A354344(n)); \\ Antti Karttunen, May 24 2022

Formula

{k | 1==A353637(k) and 0==A354344(k)}. - Antti Karttunen, May 25 2022

Extensions

Term a(1) = 1 prepended and terms a(14) .. a(56) added by Antti Karttunen, May 24 2022